There are many reasons why this is so. Let me give you a few perspectives. First, we will in a multi-cultural world. For this reason, there are so many other cultures to learn, especially non-western ones. For this reason, certain things get cut out. One of them is English grammar.
Second, by and large in the past people learned English grammar through Latin and Greek. So, when students learned Latin grammar, they de facto, learned English grammar. So, students automatically knew that they could not split an infinitive, because in Latin, an infinitive is one word. Grammatical points like this would be an given.
Third, from a linguistic perspective, language evolves. More specifically language get simpler the longer it is used. So, the English lanauge is evolving. In addition, with all the multi-culturalism, it is easy to overlook English grammar.
While I don't feel that underemphasis is universal, I'll give you a few ideas from my own experience and those I've heard from others at our English department meetings.
I'll start by referring you to state standards. In Indiana, for example, one of the specific standards in early elementary includes identification of nouns. That specific standard, however, doesn't reappear again until grade seven. What happens in the intervening years? Some teachers, I believe, think, "Well, it's not MY standard. If they got it, they got it, and if they didn't, I don't have time to remediate, I have to move on." Let me say at this point that this by no means is applied to ALL teachers, but it is something I've heard directly in my own corporation.
Another contributing factor, in my opinion, was the push to hollistic methods of teaching grammar that focuses on the idea that teachers can accomplish it all - reading, writing, and grammar instruction - with one reader and its accompanying grammar skill worksheet as the tool for this. Grammar is complex, and I don't feel that a good foundation can be built in this way. Integrate correct grammar ONCE IT IS LEARNED, yes, but the correct foundation has to be laid first. Again, I have seen this in my own corporation and with my own child's homework.
The point I will finish with is that I don't think many teacher preparation colleges fully prepare our future educators. When I was in school for my BS in English Education (and I went to a school with some renown for preparing teachers), I can't honestly think of a class that addressed the HOW of teaching English skills. I wrote papers, but I never heard the topic addressed of how to teach young people to write. I took classes that studied educational philosophies, but I never had a class that broke down anything into practical applications. I took a teaching strategies class that did nothing beyond having us create a notebook of teaching strategies that we had printed off the Internet. Many teacher say the same thing: "Everything I learned about teaching, I learned once I was already a teacher." Part of this sentiment is understandable - practical experience is invaluable, but it would seem that the college or university handing out diplomas in education should be contributing SOMETHING more. I had a conversation with the head of the education department after I graduated and had my first interview (dismal...) during which I mentioned they had questioned me about Six Traits instruction. I knew nothing - had never heard of it (this has been about seven years ago or so) - and her response was to blow it off as a fad. Whether she believed it to be a fad or not, it was a very prevalent method for writing instruction that I, buried in the academia of college, had never been exposed to.
Tied into the above point, I don't think that a lot of teachers feel comfortable teaching grammar because they don't feel they have a firm foundation in it themselves. It creates a loop - as students in primary and secondary school we aren't well-versed in grammar and writing, then in post-secondary institutions we experience more of the same. When these students go on to be teachers, they feel unprepared to tackle thorough grammar and writing instruction, so they don't, and the loop begins again.